Finite Group Databasebeta

← #14654498

Subgroups — #14654498

Order 2816.

510 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079437C211yesmaximal, characteristic
2C2×#10622657C211yesmaximal, characteristic
3C2×#10622334C211yesmaximal, characteristic
4#13068694C211yesmaximal, characteristic
5#13066981C211yesmaximal, characteristic
6#13066504C211yesmaximal, characteristic
7C11×#1472C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C4⋊Dic11C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C11×#407C2211yescharacteristic
12C2×C11×C22⋊C8C2211yescharacteristic
13#10622841—21no—
14C2×#66899—21no—
15#10622820C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66881—21no—
18C2×#66880—21no—
19#10622665—22no—
20#10622663—21no—
21#10622657—22no—
22#10622657—22no—
23#10622656—21no—
24#10622584—21no—
25C2×#66871—21no—
26#10622334—22no—
27#10622334—22no—
28C11×#324—22no—
29#10622192—22no—
30#10622107—22no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—21no—
34C22×Dic22D411yescharacteristic
35C2×C11×M16—21no—
36C22×C8×C11—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C22⋊Dic11—21no—
45C2×#4326—22no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11D411yescharacteristic
52C2×C4⋊Dic11D412yes—
53#66977—21no—
54#66977—21no—
55#66977—21no—
56#66977—21no—
57C2×Dic11⋊C4—21no—
58C2×#4318D412yes—
59C22×C11⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8D412yes—
64#66899—24no—
65#66899—22no—
66C22⋊(C11⋊C8)—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)D412yes—
70#66881—24no—
71#66880—24no—
72#66874—22no—
73#66872—22no—
74#66871—24no—
75#9995—111nomaximal, Sylow
76C24×C11#4111yescharacteristic
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—42no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—42no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—22no—
92C22×Dic11—41no—
93C22×Dic11—41no—
94C22×Dic11—82no—
95C2×Dic22—21no—
96C2×Dic22—21no—
97C2×Dic22—42no—
98C11×M16—42no—
99C2×C8×C11—22no—
100C2×C8×C11—42no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C22⋊Dic11—41no—
109C22⋊Dic11—41no—
110#4326—82no—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—22no—
114C4⋊Dic11—21no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117Dic11⋊C4—41no—
118Dic11⋊C4—41no—
119#4318—42no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—42no—
123#3195—111no—
124C2×#484—111no—
125C2×#483—111no—
126#1821—111no—
127#1472—111no—
128#1472D1111yescharacteristic
129#1298—111no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—41no—
133C23×C11#12111yescharacteristic
134C23×C11#12111yescharacteristic
135C23×C11#12111yescharacteristic
136Q8×C11—42no—
137Q8×C11—42no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—81no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12711yescharacteristic
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155C2×Dic11—42no—
156C2×Dic11—82no—
157C2×Dic11—82no—
158C2×Dic11—81no—
159C2×Dic11—82no—
160Dic22—42no—
161Dic22—42no—
162C8×C11—42no—
163C8×C11—81no—
164C11⋊C8—42no—
165C11⋊C8—42no—
166C2×C22⋊Q8—111no—
167C2×C22⋊Q8C2×D1111yescharacteristic
168C22×C4⋊C4—111no—
169#484—222no—
170#484—222no—
171#483—222no—
172#483—221no—
173#483—221no—
174#483—222no—
175#470—222no—
176#451—221no—
177#451—221no—
178C2×#107—221no—
179C2×#106—221no—
180C2×#103—221no—
181C2×#103—221no—
182#407—111no—
183#407C2×D1111yescharacteristic
184C2×C22⋊C8—111no—
185C2×C22⋊C8C2×D1111yescharacteristic
186#343—222no—
187#324—22no—
188#324—222no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—44no—
197C22×C11#39211yescharacteristic
198C22×C11#47112yes—
199C22×C11#47312yes—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11#45812yes—
206Dic11—82no—
207Dic11—81no—
208Dic11—81no—
209C22×Q8—111no—
210C22×Q8D4411yescharacteristic
211C23×C4—221no—
212C23×C4C22×D1111yescharacteristic
213C2×Q16—222no—
214C2×M16—21no—
215C2×M16—112no—
216C22×C8—21no—
217C22×C8—221no—
218C22⋊Q8—21no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C22⋊Q8—221no—
223C22⋊Q8—221no—
224C22⋊Q8—221no—
225C22⋊Q8—221no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—112no—
228C2×C4⋊C4—111no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4D4411yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—221no—
238#107—224no—
239#106—222no—
240#106—224no—
241#103—222no—
242#103—224no—
243#103—224no—
244#103—222no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248C22⋊C8—112no—
249C22⋊C8—221no—
250C22⋊C8—221no—
251C22⋊C8—221no—
252C22⋊C8C22⋊D1112yes—
253C2×C11—22no—
254C2×C11—22no—
255C2×C11—41no—
256C2×C11#201911yescharacteristic
257C2×C11#202011yescharacteristic
258C2×C11#202211yescharacteristic
259C24#433911yescharacteristic
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—42no—
263C2×Q8—221no—
264C2×Q8—221no—
265C2×Q8—442no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—222no—
272C22×C4—441no—
273C22×C4—441no—
274C22×C4—882no—
275C22×C4C2×D4411yescharacteristic
276C22×C4D4×D1111yescharacteristic
277C22×C4D4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281Q16—882no—
282M16—42no—
283M16—442no—
284C2×C8—22no—
285C2×C8—42no—
286C2×C8—41no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—442no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—221no—
295C4⋊C4—222no—
296C4⋊C4—222no—
297C4⋊C4—221no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C11#999511yescharacteristic, complemented, Sylow
307C23—22no—
308C23—22no—
309C23—41no—
310C23#6693711yescharacteristic
311C23#6693711yescharacteristic
312C23#6698311yescharacteristic
313Q8—42no—
314Q8—42no—
315Q8—442no—
316Q8—442no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4—882no—
332C2×C4—882no—
333C2×C4—882no—
334C2×C4—881no—
335C2×C4#6693511yescharacteristic
336C2×C4#6693511yescharacteristic
337C2×C4#6699011yescharacteristic
338C2×C4#6699311yescharacteristic
339C8—42no—
340C8—81no—
341C8—442no—
342C8—442no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—44no—
351C22#1062236812yes—
352C22#1062257311yescharacteristic
353C22#1062275412yes—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—81no—
358C4—81no—
359C4—882no—
360C4—881no—
361C4—881no—
362C4#1062235512yes—
363C2—22no—
364C2—22no—
365C2—41no—
366C2#1306973111yescharacteristic
367C2#1306973611yescharacteristic
368C2#1306974611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1472C2
socleC22×C11#392
prime radicalC24×C11#41
hypercenter#1472D11
hypocenterC11#9995
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
306. C11#9995semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130794372
C2×#106226572
C2×#106223342
#130686942
#130669812
#130665042
C11×#14722
#999511